Signal detection by a receiver in a multiple antenna time-dispersive system

ABSTRACT

In a MIMO system the bit error rate floor caused by time dispersion is reduced by employing a joint minimum mean square error (MMSE) equalizer for all of the respective transmit antenna—receive antenna pairings that are possible in the MIMO system. The resulting joint equalization compensates not only for the impact of the channel on the transmit antenna—receive antenna pairings but also for the interference of the other transmit antennas on any given receive antenna. The joint equalization outperforms simply replicating the prior art minimum mean square error (MMSE) equalizer for each transmit antenna—receive antenna pairings.

TECHNICAL FIELD

This invention relates to the art of wireless communications, and moreparticularly, to wireless communication systems using multiple antennasat the transmitter and multiple antennas at the receiver, so calledmultiple-input multiple-output (MIMO) systems.

BACKGROUND OF THE INVENTION

It has previously been assumed for MIMO systems that the time dispersionbetween one or more of the transmit antennas and one or more of thereceive antennas was negligible, i.e., the various paths werenonresolvable, as often occurs in low bandwidth systems, because thepulse width is longer than the channel time dispersion. However, it hasbeen recognized that under typical urban (TU) conditions, i.e., theconditions of the so-called “TU” model, that the time dispersion betweenone or more of the transmit antennas and one or more of the receiveantennas is nonnegligible. Such a non negligible time dispersion causesthe various paths to interfere with each other, resulting in a bit errorrate floor, i.e., minimum, and so the resulting bit error rate isunacceptable.

I. Ghauri and D. Slock have shown, in “Linear Receivers for the DS-CDMADownlink Exploiting Orthogonality of Spreading Codes”, 32^(nd) AsilomarConference, Nov. 1-4, 1998 pp. 650-4, that a minimum mean square error(MMSE) equalizer operating on received code division multiple access(CDMA) chips can be employed to compensate for time dispersion in asingle transmit, single receive antenna system, thus reducing the biterror rate floor and improving performance.

SUMMARY OF THE INVENTION

We have recognized, in accordance with the principles of the invention,that in a MIMO system the bit error rate floor caused by time dispersioncan be reduced by employing a joint equalizer for all of the respectivetransmit antenna—receive antenna pairings that are possible in the MIMOsystem. Advantageously, the resulting joint equalization compensates notonly for the impact of the channel on the transmit antenna—receiveantenna pairings but also for the interference of the other transmitantennas on any given receive antenna. In a particular embodiment of theinvention, the joint equalizer is a joint minimum mean square error(MMSE) equalizer, and in such an embodiment the joint equalizationoutperforms simply replicating the prior art minimum mean square error(MMSE) equalizer for each transmit antenna—receive antenna pairing.

In one embodiment of the invention, which is especially useful for CDMA,after the equalization is completed the resulting chip streams, one foreach transmit antenna, are despread in the conventional manner and thenthe resulting depread symbols may be further processed in theconventional manner. Alternatively, instead of further processing thedespread symbols in the conventional manner, the despread symbols may beprocessed, in accordance with an aspect of the invention, so as to havetheir soft bits computed through the use of a posteriori probability(APP) metric. Prior to computing the soft bits, the despread symbols maybe spatially whitened using a spatial whitening filter.

In another embodiment of the invention, which is also especially usefulfor CDMA, the equalizer is iteratively computed so that a symbol fromone transmit antenna is determined during each iteration. Initially thereceived samples are stored in a memory. After a symbol for an antennais determined, the received samples for each of the remaining antennasare then recomputed by subtracting out the determined symbol from thesamples as they existed prior to determining the symbol. Once all thesymbols for all of the transmit antennas are determined for a symbolperiod are determined the operation begins anew with the samplescorresponding to the next symbol period.

BRIEF DESCRIPTION OF THE DRAWING

In the drawing:

FIG. 1 shows an embodiment a multiple-input multiple-output (MIMO)wireless system in which the bit error rate floor caused by timedispersion is reduced by employing a joint minimum mean square error(MMSE) equalizer for all of the respective transmit antenna—receiveantenna pairings that are possible in the MIMO system, in accordancewith the principles of the invention;

FIG. 2 shows an exemplary process, in flow chart form, for the overalloperation of system of FIG. 1;

FIG. 3 shows in more detail the process by which the weights employed bythe joint equalizer of FIG. 1 are determined;

FIG. 4 shows another exemplary process, in flow chart form, for theoverall operation of system of FIG. 1;

FIG. 5 shows another embodiment a multiple-input multiple-output (MIMO)wireless system in which the bit error rate floor caused by timedispersion is reduced by employing a joint minimum mean square error(MMSE) equalizer for all of the respective transmit antenna—receiveantenna pairings that are possible in the MIMO system, in accordancewith the principles of the invention;

FIG. 6 shows a more detailed version of a buffer-subtractor of FIG. 5;

FIG. 7 shows an exemplary process, in flow chart form, for the overalloperation of system of FIG. 5;

FIG. 8 shows a particular embodiment of the joint equalizer of FIG. 1,in which the equalization is performed in the discrete frequency domain,in accordance with an aspect of the invention; and

FIG. 9 shows a particular embodiment of the joint equalizer of FIG. 1,in which the equalization is calculated in the discrete frequency domainand applied in the time domain.

DETAILED DESCRIPTION

The following merely illustrates the principles of the invention. Itwill thus be appreciated that those skilled in the art will be able todevise various arrangements which, although not explicitly described orshown herein, embody the principles of the invention and are includedwithin its spirit and scope. Furthermore, all examples and conditionallanguage recited herein are principally intended expressly to be onlyfor pedagogical purposes to aid the reader in understanding theprinciples of the invention and the concepts contributed by theinventor(s) to furthering the art, and are to be construed as beingwithout limitation to such specifically recited examples and conditions.Moreover, all statements herein reciting principles, aspects, andembodiments of the invention, as well as specific examples thereof, areintended to encompass both structural and functional equivalentsthereof. Additionally, it is intended that such equivalents include bothcurrently known equivalents as well as equivalents developed in thefuture, i.e., any elements developed that perform the same function,regardless of structure.

Thus, for example, it will be appreciated by those skilled in the artthat any block diagrams herein represent conceptual views ofillustrative circuitry embodying the principles of the invention.Similarly, it will be appreciated that any flow charts, flow diagrams,state transition diagrams, pseudocode, and the like represent variousprocesses which may be substantially represented in computer readablemedium and so executed by a computer or processor, whether or not suchcomputer or processor is explicitly shown.

The functions of the various elements shown in the FIGS., including anyfunctional blocks labeled as “processors”, may be provided through theuse of dedicated hardware as well as hardware capable of executingsoftware in association with appropriate software. When provided by aprocessor, the functions may be provided by a single dedicatedprocessor, by a single shared processor, or by a plurality of individualprocessors, some of which may be shared. Moreover, explicit use of theterm “processor” or “controller” should not be construed to referexclusively to hardware capable of executing software, and mayimplicitly include, without limitation, digital signal processor (DSP)hardware, network processor, application specific integrated circuit(ASIC), field programmable gate array (FPGA), read-only memory (ROM) forstoring software, random access memory (RAM), and non-volatile storage.Other hardware, conventional and/or custom, may also be included.Similarly, any switches shown in the FIGS. are conceptual only. Theirfunction may be carried out through the operation of program logic,through dedicated logic, through the interaction of program control anddedicated logic, or even manually, the particular technique beingselectable by the implementor as more specifically understood from thecontext.

In the claims hereof any element expressed as a means for performing aspecified function is intended to encompass any way of performing thatfunction including, for example, a) a combination of circuit elementswhich performs that function or b) software in any form, including,therefore, firmware, microcode or the like, combined with appropriatecircuitry for executing that software to perform the function. Theinvention as defined by such claims resides in the fact that thefunctionalities provided by the various recited means are combined andbrought together in the manner which the claims call for. Applicant thusregards any means which can provide those functionalities as equivalentas those shown herein.

Software modules, or simply modules which are implied to be software,may be represented herein as any combination of flowchart elements orother elements indicating performance of process steps and/or textualdescription. Such modules may be executed by hardware which is expresslyor implicitly shown.

Unless otherwise explicitly specified herein, the drawings are not drawnto scale.

In the description, identically numbered components within differentones of the FIGS. refer to the same components.

FIG. 1 shows an exemplary embodiment of a multiple-input multiple-output(MIMO) wireless system in which the bit error rate floor caused by timedispersion is reduced by employing a joint minimum mean square error(MMSE) equalizer for all of the respective transmit antenna—receiveantenna pairings that are possible in the MIMO system, in accordancewith the principles of the invention. Shown in FIG. 1 are a) transmitter101; b) transmit antennas 103; including transmit antennas 103-1 through103-M; c) receive antennas 105; including receive antennas 105-1 through105-N; d) receiver front-end 107; e) joint equalizer 109; f) optionaldespreaders 111; g) soft bit mapper 112, which may include optionalspatial whitening filter 113; and optional a posteriori probability(APP) metric processor 115.

Transmitter 101 is a MIMO transmitter, e.g., one in which an originaldata stream is divided into substreams and each resulting substream istransmitted as a modulated radio signal via an individual one oftransmit antennas 103. The transmitted signals pass to the receiver overa time dispersive channel such that signals from each transmit antenna103 reach each of receive antennas 105.

Receive antennas 105 convert the radio signals impinging upon them intoelectrical signals, which are supplied to receiver front-end 107.Receiver front-end 107 operates conventionally to produce a plurality ofstreams of binary numbers, each stream representing samples of the radiosignals received at an associated one of antennas 105. Typicallyreceiver front-end 107 performs radio frequency downconversion,filtering, sampling, and analog-to-digital conversion. The resultingsamples are provided to joint equalizer 109.

Joint equalizer 109 compensates for the effects of the transmit signalsfrom each of antennas 103 having passed through the channel as well asthe interference that results from transmitting via multiple antennassimultaneously. The output of joint equalizer 109 is M, i.e., the numberof transmit antennas, streams of corrected symbols, or in the case ofCDMA, streams of corrected chips which when properly combined formsymbols. Operation of joint equalizer 109 will be described more fullyhereinbelow. If CDMA is employed, the output of joint equalizer 109 issupplied to optional despreaders 111, which produces symbols from thestream of chips supplied by joint equalizer 109.

The symbols produced may then be further processed in the conventionalmanner for a MIMO system, e.g., soft bits may be developed by soft bitmapper 112 for use in a decoder, e.g., the well known “Turbo decoder”.Alternatively, the symbols may be supplied within soft bit mapper 112 tooptional spatial whitening filter 113, which makes the noise equal oneach branch. Note that the whitening is performed only in the spacedomain. If whitening is performed in the time domain some temporaldispersion will be introduced into the signal. The symbols, or whitenedsymbols if optional spatial whitening filter 113 is employed, mayfurther be supplied to optional a posteriori probability (APP) metricprocessor 115 within soft bit mapper 112, in accordance with an aspectof the invention. APP metric processor 115 performs a particular type ofmapping from symbols to soft bits. Operation of APP metric processor 115is described more fully hereinbelow.

FIG. 2 shows an exemplary process, in flow chart form, for the overalloperation of system of FIG. 1. Prior to performing the process of FIG.2, initial values of parameters M, N, L, P, E, and d must be determined.What each of these parameters represents is listed in Table 1.Additionally, prior to performing the process of FIG. 2 it is necessaryto determine noise covariance R_(pp), which contains samples of theautocorrelation of the chip pulse shape r(t), when CDMA is employed, orthe symbol pulse shape autocorrelation, when CDMA is not employed.

TABLE 1 Parameter Definitions M number of transmit antennas N number ofreceive antennas L length of the channel impulse response (chips) Pover-sampling factor E length of the equalizer (chips) d equalizer delay(chips) σ_(n) ² power of interference + noise (RF bandwidth) σ_(x) ²power of downlink signal (RF bandwidth) G Number of CDMA chips persymbol

The process of FIG. 2 is executed periodically, with a periodicity thatpreferably does not exceed the coherence time, T_(co), which is the timeduration for which the channel properties are substantially constant.The process is entered in step 201, in which L*P discrete channelestimations h_(o) to h_(LP-1) are developed. The channel estimate may beobtained using any conventional technique, e.g., by using correlatorstuned to the pilot channel. Each of discrete channel estimations istaken with a time spacing of the chip duration divided by P, for CDMA,or symbol duration divided by P for TDMA. Also, in step 201, thebackground noise plus interference power σ_(n) ² and the power of thedownlink from the base station to the terminal σ_(x) ² are determined inthe conventional manner. In step 203, the weights employed by jointequalizer 109 are determined, as will be described fully furtherhereinbelow.

Next, in step 205, a set of P samples from each antenna is obtained.Thereafter, in step 207, the determined weights of joint equalizer 109are applied to the samples from each antenna by joint equalizer 109. Thesamples are then despread by despreader 111, if CDMA was employed, inoptional step 209. In optional step 211, conventional soft mapping ofthe symbols to soft bits is performed, and the resulting soft bits aresupplied as an output for use by a decoder. Thereafter, conditionalbranch point 213 tests to determine whether one coherence time haselapsed since the previous execution of step 201. If the test result instep 213 is NO, indicating that the channel is believed to still remainsubstantially the same as when it was last estimated, control passes tostep 205, and the process continues as described above. If the testresult in step 213 is YES, indicating that sufficient time has passedsuch that the channel may have changed enough so as not to be consideredsubstantially the same as when it was last estimated, control passesback to step 201 and the process continues as described above.

FIG. 3 shows in more detail the process of step 203 by which the weightsemployed by joint equalizer 109. Note that the process requires the useof several matrices, and the dimensions of the various matrices aregiven in Table 2.

TABLE 2 Matrix Dimension R_(p) EP × EP R_(pp) NEP × NEP Γ(h_(n,m)) EP ×(E + L − 1) Γ(H) NEP × M(E + L − 1) Γ(H_(m)) NEP × M(E + L − 1) e_(d)(E + L − 1) × 1 A M × M(E + L − 1) a_(m) 1 × M(E + L − 1) W M × NEPw_(m) 1 × NEP Q M × M

In step 301, the channel estimates h_(o) to h_(LP-1) for each transmitand receive pair obtained in step 201 are arranged in a respectivematrix h_(n,m) as shown in equation 1. In step 303, matrix convolutionoperator Γ(h_(n,m)) is then formed for each respective matrix h_(n,m),as shown in equation 2. Thereafter, in step 305, MIMO convolutionoperator Γ(H) is then formed from the various matrix convolutionoperators as shown in equation 3.

$\begin{matrix}{h_{n,m} = \begin{bmatrix}h_{0} & h_{P} & \cdots & h_{{({L - 1})}P} \\\vdots & \vdots & \; & \vdots \\h_{P - 1} & h_{{2P} - 1} & \cdots & h_{{LP} - 1}\end{bmatrix}} & {{equation}\mspace{14mu}(1)} \\{{\Gamma\left( h_{n,m} \right)} = \begin{bmatrix}h_{n,m} & 0_{p} & \cdots & 0_{p} \\0_{p} & \; & \; & \; \\\vdots & \; & ⋰ & \vdots \\0_{p} & \cdots & 0_{p} & h_{m}\end{bmatrix}} & {{equation}\mspace{14mu}(2)} \\{{\Gamma(H)} = \begin{bmatrix}{\Gamma\left( h_{1,1} \right)} & {\Gamma\left( h_{1,2} \right)} & \cdots & {\Gamma\left( h_{1,M} \right)} \\{\Gamma\left( h_{2,1} \right)} & {\Gamma\left( h_{2,2} \right)} & \; & \vdots \\\vdots & \; & ⋰ & \; \\{\Gamma\left( h_{N,1} \right)} & \cdots & \; & {\Gamma\left( h_{N,M} \right)}\end{bmatrix}} & {{equation}\mspace{14mu}(3)}\end{matrix}$

In step 307, delay vector e_(d) is formed as shown in equation 4. Delayvector e_(d) is a one dimensional vector with E+L−1 elements which areall zero except for the single value at the E+L−1−d location, which hasa value of 1. A typical value for d, which is selectable by theimplementor, is such that the location which has a value of 1 is at thecenter of the vector. The purpose of delay vector e_(d), is to imposethe overall equalizer delay d onto the equalizer. Thereafter, in step309, delay matrix A is computed from equation 5, in which I_(M) is anidentity matrix of size M×M.e _(d)=[0 . . . 100]  equation (4)A=I _(M) ⊕e _(d)  equation (5)

Finally, in step 311, equalizer weight matrix, W, is computed inaccordance with equation 6, in which X^(H) means the Hermitian transposeof X, which is the complex conjugate transpose of the vector or matrixX.

$\begin{matrix}{W = {A\;{\Gamma(H)}^{H}\left( {{{\Gamma(H)}^{H}{\Gamma(H)}} + {\frac{\sigma_{n}^{2}}{\sigma_{x}^{2}}R_{pp}}} \right)^{- 1}}} & {{equation}\mspace{14mu}(6)}\end{matrix}$

In one embodiment of the invention, execution of step 205 is such thatthe P samples r of antenna n are initially arranged as a vector c shownin equation 7, where k is the current received chip time index if CDMAis employed, or the symbol time index if CDMA is not employed. Econsecutive in time vectors c for antenna n are then arranged as shownin equation 8, and the E consecutive in time vectors c for all of the Nantennas are further arranged as shown in equation 9, forming a vectorof received samples at time k.

$\begin{matrix}{{c_{n}(k)} = \begin{bmatrix}{r_{n}\left( {kT}_{c} \right)} \\{r_{n}\left( {{kT}_{c} + T_{s}} \right)} \\\vdots \\{r_{n}\left( {{kT}_{c} + {\left( {P - 1} \right)T_{s}}} \right)}\end{bmatrix}} & {{equation}\mspace{14mu}(7)} \\{{r_{n}(k)} = \begin{bmatrix}{c_{n}(k)} \\{c_{n}\left( {k - 1} \right)} \\\vdots \\{c_{n}\left( {k - E + 1} \right)}\end{bmatrix}} & {{equation}\mspace{14mu}(8)} \\{{r(k)} = \begin{bmatrix}{r_{1}(k)} \\{r_{2}(k)} \\\vdots \\{r_{N}(k)}\end{bmatrix}} & {{equation}\mspace{14mu}(9)}\end{matrix}$

The application of the determined weights by joint equalizer 109 in step207 may be performed as shown in equation 10, where y(k) is a resultingvector of size M×1 which contains the equalized chips if CDMA isemployed, or symbols if CDMA is not employed.y(k)=Wr(k)  equation (10)

FIG. 4 shows another exemplary process, in flow chart form, for theoverall operation of system of FIG. 1. The version of the process shownin FIG. 4 is similar to that shown in FIG. 2, but it is for embodimentsof the invention that include optional spatial whitening filter 113(FIG. 1) and optional a posteriori probability (APP) metric processor115. Unless otherwise noted, all variables and parameters employed inthe process of FIG. 4 are the same as described for FIG. 2. As with theprocess of FIG. 2, prior to performing the process of FIG. 4, initialvalues of parameters M, N, L, P, E, and d must be determined.Additionally, prior to performing the process of FIG. 4 it is necessaryto determine R_(pp).

The process of FIG. 4 is executed periodically, with a periodicity thatpreferably does not exceed the coherence time, T_(co), which is the timeduration for which the channel properties are substantially constant.The process is entered in step 401, in which L*P discrete channelestimations h_(o) to h_(LP-1) are developed. Also in step 401, thebackground noise plus interference power σ_(n) ² and the power of thedownlink from the base station to the terminal σ_(x) ² are determined inthe conventional manner. In step 403, the weights W employed by jointequalizer 109 are determined, as described hereinabove. Additionally, instep 403, the effective channel matrix H_(eff) and, optionally, spatialwhitening filter Q are determined, in accordance with an aspect of theinvention. More specifically, H_(eff) is determined as shown in equation11, and Q is determined as shown in equation 12.H _(eff)(m,n)=e _(n) ^(T) WΓ(H)e _(m) m=1:M, n=1:N  equation (11)Q=(WW ^(H))^(−1/2)  equation (12)

Next, in step 405 a set of P samples from each antenna is obtained.Thereafter, in step 407, the determined weights of joint equalizer 109are applied to the samples from each antenna by joint equalizer 109. Thesamples are then despread by despreader 111, if CDMA was employed, inoptional step 409. In step 411, whitening filter Q is applied to thedespread, equalizer outputs of step 409. In step 413, APP softbits arecomputed, in accordance with an aspect of the invention, using equations13 and 14. The softbits are the output of the process of FIG. 4, andthey may be made available to a decoder, e.g., a turbo decoder.

$\begin{matrix}\begin{matrix}{{L_{D}\left( {x_{k}❘y} \right)} = {\log_{e}\left( \frac{\Pr\left( {x_{k} = {1❘y}} \right)}{\Pr\left( {x_{k} = {{- 1}❘y}} \right)} \right)}} \\{= {{\ln\left( \frac{\sum\limits_{\hat{x},{x_{k} = 1}}{{p\left( {{y❘X} = \hat{x}} \right)}{\prod\limits_{j \neq k}{p\left( {X = x_{j}} \right)}}}}{\sum\limits_{\hat{x},{x_{k} = {- 1}}}{{p\left( {{y❘X} = \hat{x}} \right)}{\prod\limits_{j \neq k}{p\left( {X = x_{j}} \right)}}}} \right)} +}} \\{\ln\left( \frac{p\left( {x_{k} = 1} \right)}{p\left( {x_{k} = {- 1}} \right)} \right)}\end{matrix} & {{equation}\mspace{14mu} 13} \\{{p\left( {{y❘X} = x_{k}} \right)} = {\left( \frac{1}{\sqrt{2\pi}\sigma} \right)^{N_{r}}{\exp\left( {- \frac{{{y - {H_{eff}\hat{s}}}}^{2}}{2\sigma^{2}}} \right)}}} & {{equation}\mspace{14mu} 14}\end{matrix}$

Thereafter, conditional branch point 415 tests to determine whether onecoherence time has elapsed since the previous execution of step 401. Ifthe test result in step 415 is NO, indicating that the channel isbelieved to still remain substantially the same as when it was lastestimated, control passes to step 405, and the process continues asdescribed above. If the test result in step 415 is YES, indicating thatsufficient time has passed such that the channel may have changed enoughso as not to be considered substantially the same as when it was lastestimated, control passes back to step 401 and the process continues asdescribed above.

FIG. 5 shows another exemplary embodiment of a multiple-inputmultiple-output (MIMO) wireless system in which the bit error rate floorcaused by time dispersion is reduced by employing a joint minimum meansquare error (MMSE) equalizer for all of the respective transmitantenna—receive antenna pairings that are possible in the MIMO system,in accordance with the principles of the invention. Shown in FIG. 5 area) transmitter 501; b) transmit antennas 503; including transmitantennas 503-1 through 503-M; c) receive antennas 505; including receiveantennas 505-1 through 505-N; d) receiver front-end processor 507; e)buffer-subtractor 521; f) joint equalizer 523; g) optional despreader525; h) soft bit mapper 527; i) space-time regenerator 529; j) ordercontroller 531 and k) switch 533.

Transmitter 501 is a MIMO transmitter, e.g., one in which an originaldata stream is divided into substreams and each resulting substream istransmitted as a modulated radio signal via an individual one oftransmit antennas 503. The transmitted signals pass to the receiver overa time dispersive channel such that signals from each transmit antenna503 reach each of receive antennas 505.

Receive antennas 505 convert the radio signals impinging upon them intoelectrical signals, which are supplied to receiver front-end processor507. Receiver front-end processor 507 operates conventionally to producea stream of binary numbers representing samples of the radio signalsreceived at antennas 505. Typically receiver front-end processor 507performs radio frequency downconversion, filtering, sampling, andanalog-to-digital conversion. The resulting samples are provided tobuffer-substractor 521.

Buffer-subtractor 521 is shown in more detail in FIG. 6. Buffersubtractor 521 includes buffer 601, memory 603, and subtractor 605.Buffer 601 stores a time consecutive set of samples from each ofantennas 505 as those samples become available from front-end processor507. Buffer 601 supplies the samples it receives from front-endprocessor 507 to memory 603 when an entire set is stored, i.e., thecontents of buffer 601 are quickly dumped to memory 603. Once the set ofsamples are stored in memory 603 they may be independently accessed andsent to joint equalizer 523 (FIG. 5). Additionally, space time samplesfrom a second input of buffer-subtractor 521 are supplied to subtractor605. Subtractor 605 is cable of forming the difference between aspecified location in memory 603 and a second input to buffer-subtractor521. The resulting difference is stored in the specified location inmemory 603.

Joint equalizer 523 performs M passes through memory 603 with adifferent equalizer weight w_(m) in each pass. Each weight is chosen toemphasize transmit antenna m and to suppress transmit antennas m+1through M.

The output of joint equalizer 523 is supplied to conventional soft bitmapper 527, via optional conventional despreader 525 if CDMA isemployed. The soft bits developed by soft bit mapper 527 are thensupplied as an output, such as may be used by a decoder, e.g., the wellknown “Turbo decoder”.

The same output that is supplied to conventional soft bit mapper 527 mayalso be supplied to space-time regenerator 529 via switch 533.Space-time regenerator 529 forms a set of time consecutive samples foreach receive antenna assuming the soft symbol is correct. In otherwords, assuming a particular soft symbol had been the actual symboltransmitted by a particular transmit antenna, space-time regenerator 529creates the corresponding effect that such a symbol would have caused oneach of receive antennas 505 given the channel characteristics.Operation of space-time regenerator 529 will be explained more fullyhereinbelow.

Order controller 531 determines, based on channel estimates, the signalfrom which transmit antenna will be processed at any particular time, aswill be explained more fully hereinbelow.

FIG. 7 shows an exemplary process, in flow chart form, for the overalloperation of system of FIG. 5 in which switch 533 is connected betweendespreader 525 and space-time regenerator 529. Prior to performing theprocess of FIG. 7, initial values of parameters M, N, L, P, E, and dmust be determined. What each of these parameters represents is listedin Table 1. Additionally, prior to performing the process of FIG. 7 itis necessary to determine R_(pp), which is samples of theautocorrelation of the chip pulse shape r(t), when CDMA is employed, orthe symbol pulse shape autocorrelation, when CDMA is not employed.

The process of FIG. 7 is executed periodically, with a periodicity thatpreferably does not exceed the coherence time, T_(co). The process isentered in step 701, in which L*P discrete channel estimations h_(o) toh_(LP-1) are developed. The channel estimate may be obtained using anyconventional technique, e.g., by using correlators tuned to the pilotchannel. Each discrete channel estimation is taken with a time spacingof the chip duration divided by P, for CDMA, or symbol duration dividedby P for TDMA. Also in step 701, the background noise plus interferencepower σ_(n) ² and the power of the downlink from the base station to theterminal σ_(x) ² are determined in the conventional manner.

In step 703, order controller 531 determines, according to equations 15and 16, the order in which the signals from the various transmitantennas will be processed, with the signal from a respective transmitantenna being processed for each execution of joint equalizer 523. Sortis a function that rearranges the elements of vector P so that they runfrom largest to smallest and order is a list of all the antenna transmitantenna numbers as they should be processed by joint equalizer 523. Itis preferable to process the so-called “strong” signals first. However,the particular characteristic, or set of characteristics, which are usedto define the “strength” of a signal is at the discretion of theimplementer. In the particular embodiment shown herein, estimated signalpowers are employed as the strength. Further note that although hereinthe order for all the antennas is determined simultaneously, those ofordinary skill in the art will readily recognize that it is possible tosuccessively determine which antenna to process.P=∥diag(WΓ(H))∥²  equation (15)[P′,order]=sort(P)  equation (16)

In step 705, the equalizer weights for the particular antenna currentlybeing processed, m, as specified by the order, is determined accordingto equations 17 and 18, in which delay vector a_(m) is the m^(th) row ofdelay matrix A which was described hereinabove.

$\begin{matrix}{w_{m} = {a_{m}{\Gamma\left( H_{m} \right)}^{H}\left( {{{\Gamma\left( H_{m} \right)}^{H}{\Gamma\left( H_{m} \right)}} + {\frac{\sigma_{n}^{2}}{\sigma_{x}^{2}}R_{pp}}} \right)^{- 1}}} & {{equation}\mspace{14mu}(17)} \\{{\Gamma\left( H_{m} \right)} = \begin{bmatrix}0 & {\Gamma\left( h_{1,2} \right)} & 0 & {{\cdots\Gamma}\left( h_{1,M} \right)} \\0 & {\Gamma\left( h_{2,2} \right)} & 0 & \vdots \\\vdots & \vdots & \vdots & \vdots \\0 & {\Gamma\left( h_{N,2} \right)} & 0 & {{\cdots\Gamma}\left( h_{N,M} \right)}\end{bmatrix}} & {{equation}\mspace{14mu}(18)}\end{matrix}$

Note that for each iteration m of equation 18, columns corresponding toorder(1) through order(m−1) are set to the block zero matrix 0. Notethat order is vector which contains a listing of the M antenna numbersin the order in which they will be processed. Order may be the result ofthe well known function sort of MatLab®. Doing so accounts for the factthat signals from transmit antennas 1 through m−1 have already beensubtracted from the signal remaining to be processed for this set ofsamples.

Next, in step 707 a set of samples that span at least the duration of adata symbol is obtained from each receive antenna. Thereafter, in step709, counter variable m is initialized to 1. In step 711, the weightsdetermined for joint equalizer 523 in step 705 are applied to thesamples from each receive antenna by joint equalizer 523, in accordancewith equation 19.y(k)=W _(m) ^(T) r(k)  equation (19)

The samples are then despread by despreader 525, if CDMA was employed,in optional step 713. In optional step 715, conventional soft mapping ofthe symbols to soft bits is performed, and the resulting soft bits aresupplied as an output for use by a decoder.

In step 717, samples are produced by space-time regenerator 529according to equations 20 and 21.

$\begin{matrix}{{{\hat{x}}_{m}(k)} = {{{\hat{d}}_{m}(k)}\begin{bmatrix}{s\left( {k\; G} \right)} \\{s\left( {{k\; G} + 1} \right)} \\\vdots \\{s\left( {{k\; G} + G - 1} \right)}\end{bmatrix}}} & {{equation}\mspace{14mu}(20)} \\{{y_{m}(k)} = {\begin{bmatrix}{\Gamma\left( h_{1,m} \right)} \\{\Gamma\left( h_{2,m} \right)} \\\vdots \\{\Gamma\left( h_{N,m} \right)}\end{bmatrix}{{\hat{x}}_{m}(k)}}} & {{equation}\mspace{14mu}(21)}\end{matrix}$

In step 719 the output of space-time regenerator 529 is subtracted fromthe contents of memory 603 (FIG. 6), as shown by equation 22.r(k)=r(k)−y _(m)(k)  equation (22)

Thereafter, conditional branch point 721 tests to determine if m isequal to M. If the test result in step 721 is NO, indicating that notall of the transmit antennas have yet had their signal contributionprocessed, m is incremented in step 723. Thereafter, control passes backto step 711 and the process continues as described above. If the testresult in step 712 is YES, indicating that all of the transmit antennashave had their signal contribution processed, control passes toconditional branch point 725, which tests to determine whether onecoherence time has elapsed since the previous execution of step 701. Ifthe test result in step 725 is NO, indicating that the channel isbelieved to still remain substantially the same as when it was lastestimated, control passes to step 707, and the process continues asdescribed above. If the test result in step 725 is YES, indicating thatsufficient time has passed such that the channel may have changed enoughso as not to be considered substantially the same as when it was lastestimated, control passes back to step 701 and the process continues asdescribed above.

In an alternative configuration of FIG. 5, switch 533 is connected tothe output of an error correction decoder which is either directly orindirectly connected to soft bit mapping 527. Doing so may improveperformance.

FIG. 8 shows a particular embodiment of joint equalizer 109, in whichthe equalization is performed in the discrete frequency domain, inaccordance with an aspect of the invention. Shown in FIG. 8 making upjoint equalizer 109 are a) fast Fourier transform (FFT) processors 801,including EFT processors 801-1 through 801-N, where N is the number ofreceive antennas; b) channel estimators 803, including channelestimators 803-1 through 803-N; c) fast Fourier transform (FFT)processors 805, including FFT processors 805-1 through 805-N*M, where Mis the number of transmit antennas; d) MMSE detection per frequency binprocessor 807; and e) inverse fast Fourier transform (IFFT) processors809, including IFFT processors 809-1 through 809-M.

Each of FFT processors 801 receives from front-end 107 a signal of timedomain digital samples corresponding to a respective one of receiveantennas 105-N and performs the FFT algorithm on a set of consecutivesamples to convert the time domain samples to samples in the discretefrequency domain, r_(n)(ω), where ω is a particular discrete frequency.The number of samples F is at the discretion of the implementer based ona tradeoff between the performance and complexity of FFT processors 801.Typically the number of samples is a power of 2, e.g., 128, although themore samples the more accurate the equalization process will be. Thepossible values for ω are determined as

${\omega = \frac{2\pi\; n}{T_{s}F}},$where n ranges from 0 to F−1. The resulting discrete frequency samplesfor each receive antenna are supplied to MMSE detection per frequencybin processor 807.

Each of channel estimators 803 also receives from front-end 107 a signalof time domain digital samples corresponding to a respective one ofreceive antennas 105-N and performs a channel estimate for the channelbetween its respective receive antenna and each of the M transmitantennas, thereby producing M channel estimates. Each channel estimateis a series of complex numbers that defines the impulse response of thechannel. Fast Fourier transform (FFT) processors 805 each converts arespective channel estimate into the discrete frequency domainrepresentation thereof, and supplies the resulting discrete frequencydomain representation of the channel estimates h_(n,m)(ω) to MMSEdetection per frequency bin processor 807.

MMSE detection per frequency bin processor 807 performs the equalizationin the frequency domain by computingz(ω)=(H(ω)^(H) H(ω)+σ² I)⁻¹ H(ω)^(H) r(ω)  equation (23)

where

$\begin{matrix}{{H(\omega)} = \begin{bmatrix}{h_{1,1}(\omega)} & \cdots & {h_{1,M}(\omega)} \\\vdots & ⋰ & \vdots \\{h_{N,1}(\omega)} & \cdots & {h_{N,M}(\omega)}\end{bmatrix}} & {{equation}\mspace{14mu}(24)} \\{{r(\omega)} = \begin{bmatrix}{r_{1}(\omega)} \\{r_{2}(\omega)} \\\vdots \\{r_{N}(\omega)}\end{bmatrix}} & {{equation}\mspace{14mu}(25)} \\{{\sigma^{2} = \frac{\sigma_{n}^{2}}{\sigma_{x}^{2}}},} & {{equation}\mspace{14mu}(26)}\end{matrix}$

σ_(n) ² is the background noise plus interference power,

σ_(x) ² is the power of the downlink signal from the base station to theterminal, and

I is the identity matrix.

Each of the resulting M components of resulting vector z(ω) are theninverse frequency transformed from the discrete frequency domain intothe time domain by inverse fast Fourier transform (IFFT) processors 809.The time domain equalized outputs are then supplied as the output ofjoint equalizer 109.

FIG. 9 shows a particular embodiment of joint equalizer 109 in which theequalization is calculated in the discrete frequency domain and appliedin the time domain, in accordance with an aspect of the invention. Shownin FIG. 9 making up joint equalizer 109 are a) matrix finite impulseresponse (FIR) filter 901; b) channel estimators 903, including channelestimators 903-1 through 903-N; c) fast Fourier transform (FFT)processors 905, including FFT processors 905-1 through 905-N*M, where Mis the number of transmit antennas; d) MMSE tap weight calculator 907;and e) inverse fast Fourier transform (IFFT) processors 909, includingIFFT processors 909-1 through 909-N*M

Matrix finite impulse response (FIR) filter 901 continuously receivesfrom front-end 107 a signal of time domain digital samples correspondingto a respective one of receive antennas 105-N. The number of taps ofmatrix FIR filter 901 is at the discretion of the implementer based on atradeoff between performance and complexity. Typically the number ofsamples is a power of 2, e.g., 128.

Each of channel estimators 903 also receives from front-end 107 a signalof time domain digital samples corresponding to a respective one ofreceive antennas 105-N and performs a channel estimate for the channelbetween its respective receive antenna and each of the M transmitantennas, thereby producing M channel estimates. Each channel estimateis a series of complex numbers that defines the impulse response of thechannel. Fast Fourier transform (FFT) processors 905 each converts arespective channel estimate into the discrete frequency domain, andsupplies the resulting discrete frequency domain representation of thechannel estimates h_(n,m)(ω) to MMSE tap weight calculator 907. Thenumber of samples employed by FFT processors 905 for each conversionshould be the same as the number of taps in matrix FIR filter 901.

MMSE tap weight calculator 907 develops frequency domain representationsof the weights necessary to perform the equalization in the time domainby computingS(ω)=(H(ω)^(H) H(ω)+σ² I)⁻¹ H(ω)^(H)  equation (27)where H(ω), σ² are defined as explained hereinabove in connection withFIG. 8.

Each of the resulting M components of resulting vector S(ω) are groupedby frequency into frequency vectors, and are then the frequency vectorsare inverse frequency transformed from the discrete frequency domain tobecome filter weights in the time domain by inverse fast Fouriertransform (IFFT) processors 909. The weights are then supplied to matrixFIR filter 901 which utilizes them to perform equalization in the timedomain on the signals received from front-end 107 as shown by equation28,

$\begin{matrix}{{y(k)} = {\sum\limits_{j = 0}^{F - 1}{S_{j}{r\left( {k - j} \right)}}}} & {{equation}\mspace{14mu}(28)}\end{matrix}$

where y (k) is the vector output at time k, y having M components—onefor each transmit antenna—, S_(j) is the M×N filter matrix for delay j,which is the inverse Fourier transform of S(ω), r(k)is the vector inputsignal which is received by matrix FIR filter 901 as defined in equation(9), and F is the number of samples taken for each FFT.

Given the foregoing, those of ordinary skill in the art will readilyrecognize that other equalizer algorithms which approximate theoperation and performance of MMSE, such as least mean square (LMS),recursive least squares (RLS), or minimum intersymbol interference (ISI)subject to an anchor condition, can be employed in a joint manner, e.g.,in a space manner, in the implementation of joint equalizer 109.

Those of ordinary skill in the art will readily recognize that thetechniques of the instant invention may be employed in systems in whichthe various transmit antennas are transmitting at different data rates,e.g., using different encoding rates and/or transmit constellations,such as quaternary phase-shift keying (QPSK) or 16-ary quadratureamplitude modulation (16-QAM). In such a situation, if the embodiment ofFIG. 5 is employed, order controller 531 is not required because theantennas must always be processed in an a priority determined order.

1. A method for compensating for time dispersion in a receiver of awireless system that has a plurality of transmit antennas and aplurality of a receive antennas, the method comprising the steps of:receiving samples for each receive antenna; determining a jointequalizer solution using channel information for at least one pairing ofat least one of said transmit antennas and said receive antennas andsaid received samples of at least two of said receive antennas; andapplying said determined joint equalizer solution to said receivedsamples from at least one of said receive antennas to develop equalizedsamples; wherein said step of determining a joint equalizer solution isperformed at least partly in the discrete frequency domain.
 2. Theinvention as defined in claim 1 wherein said joint equalizer solution isa joint minimum mean square error (MMSE) solution.
 3. The invention asdefined in claim 1 further comprising the step of estimating a channelfor said at least one pairing of at least one of said transmit antennasand said receive antennas.
 4. The invention as defined in claim 1 saidstep of applying said determined joint equalizer solution is performedin the frequency domain.
 5. A method for compensating for timedispersion in a receiver of a wireless system that has a plurality oftransmit antennas and a plurality of receive antennas, the methodcomprising the steps of: receiving samples for each receive antenna;determining a joint equalizer solution using channel information for atleast one pairing of at least one of said transmit antennas and saidreceive antennas and said received samples of at least two of saidreceive antennas; applying said determined joint equalizer solution tosaid received samples from at least one of said receive antennas todevelop equalized samples; and despreading said equalized samples. 6.The invention as defined in claim 1 wherein at least two of saidtransmit antennas transmit at different rates.
 7. The invention asdefined in claim 1 wherein at least two of said transmit antennastransmit using different transmit constellations.
 8. The invention asdefined in claim 1 further comprising the step of performing softmapping using a version of said equalized samples.
 9. The invention asdefined in claim 8 wherein said version of said equalized samples aredespread samples.
 10. The invention as defined in claim 8 wherein saidstep of performing soft mapping further comprises the step of spatialwhitening said version of said equalized samples.
 11. The invention asdefined in claim 8 herein said step of performing soft mapping furthercomprises the step of performing a posteriori probability (APP) metricprocessing an said version of said equalized samples.
 12. The inventionas defined in claim 1 wherein said determining step is performedmultiple times, once for each one of said transmit antennas.
 13. Theinvention as defined in claim 1 wherein said determining and applyingsteps are iterated multiple times over a symbol period, and iterationfor each one of said transmit antennas, and said method furthercomprises, for each iteration, the steps of: generating a representationof signals that would have arrived had a particular symbol for acurrently being processed transmit antenna had been transmitted; andsubtracting said representation from said samples received for eachreceive antenna.
 14. The invention as defined in claim 1 wherein saidjoint equalizer solution is one from the group consisting of: a jointleast mean square (LMS) solution, a joint recursive least squares (RLS)solution, or a joint minimum intersymbol interference (ISI) subject toan anchor condition solution.
 15. A receiver for use in a multiple-inputmultiple-output (MIMO) system in which a plurality of signal detectorsreceive signals transmitted by a plurality of signal sources, saidreceiver comprising: a joint equalizer that develops a joint equalizersolution using channel information for at least one pairing of at leastone of said signal sources and said signal detectors and receivedsamples of at least two of said signal detectors and supplies as anoutput a signal that includes at least said joint equalizer solutionapplied to a signal received by at least one of said signal detectors; asoft bit mapper for developing soft bits from said joint equalizeroutput; and a despreader interposed between said joint equalizer andsaid soft bit mapper.
 16. The invention as defined in claim 15 whereinsaid joint equalizer solution is a joint minimum mean square error(MMSE) equalizer solution.
 17. The invention as defined in claim 15wherein said soft bit mapper further comprises an a posterioriprobability (APP) metric processor.
 18. The invention as defined inclaim 15 wherein said soft bit mapper further comprises a spatialwhitening unit.
 19. The invention as defined in claim 15 where at leasttwo of said transmit sources transmits signals at different rates. 20.The invention as defined in claim 15 wherein at least two of saidtransmit sources transmits signals using different transmitconstellations.
 21. The invention as defined in claim 15 furthercomprising: a space time regenerator coupled to said joint equalizer;and a buffer-subtractor coupled between said signal detectors and saidjoint equalizer and between said space time regenerator and said jointequalizer.
 22. The invention as defined in claim 21 further comprising afront end processor coupled to said buffer-subtractor.
 23. The inventionas defined in claim 1 further comprising an error correction decodercoupled to said soft bit mapper; a space time regenerator coupled tosaid error correction decoder; and a buffer-subtractor coupled betweensaid signal detectors and said joint equalizer and between said spacetime regenerator and said joint equalizer.
 24. The invention as definedin claim 23 further comprising a front end processor coupled to saidbuffer-subtractor.
 25. The invention as defined in claim 15 furthercomprising an order controller for determining an order in which signalsfrom said signal detectors will be processed by said joint equalizer.26. A receiver for use in a multiple-input multiple-output (MIMO) systemin which a plurality of signal detectors receive signals transmitted bya plurality of signal sources, said receiver comprising: a jointequalizer that develops a joint equalizer solution using channelinformation for at least one pairing of said at least one of said signalsources and said signal detectors and received samples of at least twoof said signal detectors and supplies as an output a signal thatincludes at least said equalizer solution applied to a signal receivedby at least one of said signal detectors; and a soft bit mapper fordeveloping soft bits from said joint equalizer output; wherein saidjoint equalizer solution is a joint minimum mean square error (MMSE)equalizer solution and wherein said join equalizer further comprises: afirst plurality of fast Fourier transform processors, each of said fastFourier transform processors being coupled to receive a respective inputcorresponding to a signal received by one of said signal detectors andsupplying as an output a discrete frequency domain representationthereof; a plurality of channel estimation units each of which iscoupled to receive a is respective input corresponding to a signalreceived by one of said signal detectors which develops a channelestimate for each channel between each respective signal source and eachrespective signal detector; a second plurality of fast Fourier transformprocessors, each of said second plurality of fast Fourier transformprocessors coupled to receive a respective input corresponding to achannel estimate for a respective one of said channels between saidsignal sources and said signal detectors and supplying as an output adiscrete frequency domain representation thereof; an MMSE detection perfrequency bin processor coupled to receive as inputs said outputs fromsaid first plurality of fast Fourier transform processors and from saidsecond plurality of fast Fourier transform processors to produce adiscrete frequency domain representation of an application of said jointminimum mean square error (MMSE) equalizer solution to said signalsreceived by each of said signal detectors; and a plurality of inversefast Fourier transform processors which convert said discrete frequencydomain representation of an application of said joint minimum meansquare error (MMSE) equalizer solution to the time domain.
 27. Theinvention as defined in claim 26 wherein M is the number of signalsources and N is the number of signal detectors, and wherein said MMSEdetection per frequency bin processor performs the equalization in thefrequency domain by computingz(ω)=(H(ω)^(H) H(ω)+σ² I)⁻¹ H(ω)^(H) r(ω) where${H(\omega)} = \begin{bmatrix}{h_{1,1}(\omega)} & \cdots & {h_{1,M}(\omega)} \\\vdots & ⋰ & \vdots \\{h_{N,1}(\omega)} & \cdots & {h_{N,M}(\omega)}\end{bmatrix}$ ${r(\omega)} = \begin{bmatrix}{r_{1}(\omega)} \\{r_{2}(\omega)} \\\vdots \\{r_{N}(\omega)}\end{bmatrix}$ $\sigma^{2} = \frac{\sigma_{n}^{2}}{\sigma_{x}^{2}}$ σ²is the background noise plus interference power, σ_(x) ² is the sum ofthe power received by all said signal detectors from all of said signalsources, each r(ω) is said output of a one of said first plurality offirst Fourier transform processors, each h(ω) is said output of a one ofsaid second plurality of first Fourier transform processors, I is theidentity matrix, X^(H) means the Hermitian transpose of X, which is thecomplex conjugate transpose of the vector or matrix X, and z(ω) is theequalized output vector in the discrete frequency domain for frequencyω.
 28. A receiver for use in a multiple-input multiple-output (MIMO)system in which a plurality of signal detectors receive signalstransmitted by a plurality of signal sources, said receiver comprising:a joint a equalizer that develops a joint equalizer solution usingchannel information for at least one pairing of said at least one ofsaid signal sources and said signal detectors and received samples of atleast two of said signal detectors and supplies as an output a signalthat includes at least said equalizer solution applied to a signalreceived by at least one of said signal detectors; and a soft bit mapperfor developing soft bits from said joint equalizer output; wherein saidjoint equalizer solution is a joint minimum mean square error (MMSE)equalizer solution and wherein said joint equalizer further comprises: aplurality of channel estimation units each of which coupled to receive arespective input corresponding to a signal received by one of saidsignal detectors which develops a channel estimate for each channelbetween each respective signal source and each respective signaldetector; a plurality of fast Fourier transform processors, each of saidplurality of fast Fourier transform processors being coupled to receivea respective input corresponding to a channel estimate for a respectiveone of said channels between said signal sources and said signaldetectors and supplying as an output a discrete frequency domainrepresentation thereof; an MMSE tap weight calculator coupled to receiveas inputs said outputs from said plurality of fast Fourier transformprocessors to produce a discrete frequency domain representation of ajoint minimum mean square error (MMSE) equalizer solution to saidsignals received by each of said signal detectors; a plurality ofinverse fast Fourier transform processors which convert said discretefrequency domain representation of a joint minimum mean square error(MMSE) equalizer solution to matrices of filter coefficients in the timedomain; and a matrix finite impulse response (FIR) fitter coupled toapply said matrices of filter coefficients in the time domain to saidsignals received by said signal detectors.
 29. The invention as definedin claim 28 wherein M is the number of signal sources and N is thenumber of signal detectors, and wherein said MMSE equalizer solution isdeveloped by computing:S(ω)=(H(ω)^(H) H(ω)+σ² I)⁻¹ H(ω)^(H) where${H(\omega)} = \begin{bmatrix}{h_{1,1}(\omega)} & \cdots & {h_{1,M}(\omega)} \\\vdots & ⋰ & \vdots \\{h_{N,1}(\omega)} & \cdots & {h_{N,M}(\omega)}\end{bmatrix}$ $\sigma^{2} = \frac{\sigma_{n}^{2}}{\sigma_{x}^{2}}$σ_(n) ² is the background noise plus interference power, σ_(x) ² is thesum of the power received by all said signal detectors from all of saidsignal sources, each h(ω) is said output of a one of said plurality offast Fourier transform processors, I is the identity matrix, X^(H) meansthe Hermitian transpose of X, which is the complex conjugate transposeof the vector or matrix X, and S(ω) is a frequency domain matrixrepresenting the equalization for frequency ω.
 30. The invention asdefined in claim 29 wherein said matrix FIR filter applies said matricesof filter coefficients in the time domain to said signals received bysaid signal detectors by computing${y(k)} = {\sum\limits_{j = 0}^{F - 1}{S_{j}{r\left( {k - j} \right)}}}$where y(k) is a vector output at time k, y having one component for eachof said signal sources, S_(j) is a M×N filter matrix for delay j, whichis the inverse Fourier transform of S(ω), r(k) is a vector of receivedsamples at time k, and F is the number of samples taken for each fastFourier transform by each of said plurality of fast Fourier transformprocessors.
 31. The invention as defined in claim 15 wherein said MIMOsystem is a wireless system, said signal sources are transmit antennasand said detectors are antennas of said receiver.
 32. The invention asdefined in claim 15 wherein said joint equalizer develops said jointequalizer solution as a function of estimates of the channels betweeneach of said signal sources and said signal detectors.
 33. The inventionas defined in claim 15 wherein said joint equalizer develops and appliessaid joint equalizer solution in a time domain.
 34. The invention asdefined in claim 15 wherein said joint equalizer develops and appliessaid joint equalizer solution in a frequency domain.
 35. The inventionas defined in claim 16 wherein said joint equalizer develops and appliessaid joint equalizer solution in a discrete frequency domain and appliessaid joint minimum mean square error (MMSE) equalizer solution in a timedomain.
 36. The invention as defined in claim 16 wherein said jointequalizer develops said joint minimum mean square error (MMSE) equalizersolution by computing$W = {A\;\left( {\Gamma(H)} \right)^{H}\left( {{\left( {\Gamma(H)} \right)^{H}{\Gamma(H)}} + {\frac{\sigma_{n}^{2}}{\sigma_{x}^{2}}R_{pp}}} \right)^{- 1}}$where Γ(H) is a MIMO convolution operator, X^(H) means the Hermitiantranspose of X, which is the complex conjugate transpose of the vectoror matrix X, A is a delay matrix, σ_(n) ² is the background noise plusinterference power, σ_(x) ² is the sum of the power received by all saidsignal detectors from all of said signal sources, noise covarianceR_(pp), and said joint equalizer applies said joint minimum mean squareerror (MMSE) equalizer solution by computingy(k)=Wr(k) where r(k) is a vector of received samples at time k, and isy(k) is the vector output at time k representing the application of saidjoint minimum mean square error (MMSE) equalizer to said vector ofreceived samples at time k.
 37. The invention as defined in claim 15wherein said joint equalizer solution is one from the group consistingof: a joint least mean square (LMS) solution, a joint recursive leastsquares (RLS) solution, or a joint minimum intersymbol interference(ISI) subject to an anchor condition solution.
 38. A receiver for use ina multiple-input multiple-output (MIMO) system in which a plurality ofreceive antennas receive signals transmitted by a plurality of transmitantennas, said receiver comprising: means for (i) developing a jointequalizer solution using channel information for at least one pairing ofat least one of said transmit antennas and said receive antennas andsaid received samples of at least two of said receive antennas, saidjoint equalizer solution being developed at least partly in a frequencydomain, and (ii) supplying as an output a signal that includes at leastsaid joint equalizer solution applied to signal received by at least oneof said receive antennas; and means for developing soft bits from saidoutput signal.